Properties

Label 230.5.f.a.47.15
Level $230$
Weight $5$
Character 230.47
Analytic conductor $23.775$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [230,5,Mod(47,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("230.47");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 230.f (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(23.7750915093\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.15
Character \(\chi\) \(=\) 230.47
Dual form 230.5.f.a.93.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.00000 - 2.00000i) q^{2} +(4.47696 - 4.47696i) q^{3} +8.00000i q^{4} +(-20.9409 + 13.6558i) q^{5} -17.9078 q^{6} +(-15.4160 - 15.4160i) q^{7} +(16.0000 - 16.0000i) q^{8} +40.9136i q^{9} +O(q^{10})\) \(q+(-2.00000 - 2.00000i) q^{2} +(4.47696 - 4.47696i) q^{3} +8.00000i q^{4} +(-20.9409 + 13.6558i) q^{5} -17.9078 q^{6} +(-15.4160 - 15.4160i) q^{7} +(16.0000 - 16.0000i) q^{8} +40.9136i q^{9} +(69.1933 + 14.5701i) q^{10} +133.641 q^{11} +(35.8157 + 35.8157i) q^{12} +(-27.8077 + 27.8077i) q^{13} +61.6638i q^{14} +(-32.6150 + 154.888i) q^{15} -64.0000 q^{16} +(-6.97609 - 6.97609i) q^{17} +(81.8272 - 81.8272i) q^{18} -581.940i q^{19} +(-109.246 - 167.527i) q^{20} -138.033 q^{21} +(-267.283 - 267.283i) q^{22} +(-77.9968 + 77.9968i) q^{23} -143.263i q^{24} +(252.039 - 571.928i) q^{25} +111.231 q^{26} +(545.803 + 545.803i) q^{27} +(123.328 - 123.328i) q^{28} -1422.24i q^{29} +(375.006 - 244.546i) q^{30} -109.874 q^{31} +(128.000 + 128.000i) q^{32} +(598.307 - 598.307i) q^{33} +27.9044i q^{34} +(533.340 + 112.306i) q^{35} -327.309 q^{36} +(347.767 + 347.767i) q^{37} +(-1163.88 + 1163.88i) q^{38} +248.988i q^{39} +(-116.561 + 553.546i) q^{40} -1500.74 q^{41} +(276.067 + 276.067i) q^{42} +(687.304 - 687.304i) q^{43} +1069.13i q^{44} +(-558.708 - 856.766i) q^{45} +311.987 q^{46} +(-97.5012 - 97.5012i) q^{47} +(-286.526 + 286.526i) q^{48} -1925.70i q^{49} +(-1647.93 + 639.777i) q^{50} -62.4634 q^{51} +(-222.461 - 222.461i) q^{52} +(2457.09 - 2457.09i) q^{53} -2183.21i q^{54} +(-2798.56 + 1824.98i) q^{55} -493.310 q^{56} +(-2605.32 - 2605.32i) q^{57} +(-2844.48 + 2844.48i) q^{58} -3828.70i q^{59} +(-1239.10 - 260.920i) q^{60} -5066.25 q^{61} +(219.748 + 219.748i) q^{62} +(630.722 - 630.722i) q^{63} -512.000i q^{64} +(202.581 - 962.051i) q^{65} -2393.23 q^{66} +(1522.51 + 1522.51i) q^{67} +(55.8087 - 55.8087i) q^{68} +698.377i q^{69} +(-842.068 - 1291.29i) q^{70} -1397.47 q^{71} +(654.618 + 654.618i) q^{72} +(1262.48 - 1262.48i) q^{73} -1391.07i q^{74} +(-1432.13 - 3688.87i) q^{75} +4655.52 q^{76} +(-2060.21 - 2060.21i) q^{77} +(497.975 - 497.975i) q^{78} -5010.15i q^{79} +(1340.21 - 873.970i) q^{80} +1573.07 q^{81} +(3001.47 + 3001.47i) q^{82} +(3638.73 - 3638.73i) q^{83} -1104.27i q^{84} +(241.349 + 50.8213i) q^{85} -2749.21 q^{86} +(-6367.32 - 6367.32i) q^{87} +(2138.26 - 2138.26i) q^{88} -12022.9i q^{89} +(-596.117 + 2830.95i) q^{90} +857.363 q^{91} +(-623.974 - 623.974i) q^{92} +(-491.903 + 491.903i) q^{93} +390.005i q^{94} +(7946.84 + 12186.3i) q^{95} +1146.10 q^{96} +(897.842 + 897.842i) q^{97} +(-3851.39 + 3851.39i) q^{98} +5467.75i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 2.00000i −0.500000 0.500000i
\(3\) 4.47696 4.47696i 0.497440 0.497440i −0.413200 0.910640i \(-0.635589\pi\)
0.910640 + 0.413200i \(0.135589\pi\)
\(4\) 8.00000i 0.500000i
\(5\) −20.9409 + 13.6558i −0.837634 + 0.546231i
\(6\) −17.9078 −0.497440
\(7\) −15.4160 15.4160i −0.314611 0.314611i 0.532082 0.846693i \(-0.321410\pi\)
−0.846693 + 0.532082i \(0.821410\pi\)
\(8\) 16.0000 16.0000i 0.250000 0.250000i
\(9\) 40.9136i 0.505106i
\(10\) 69.1933 + 14.5701i 0.691933 + 0.145701i
\(11\) 133.641 1.10447 0.552237 0.833687i \(-0.313774\pi\)
0.552237 + 0.833687i \(0.313774\pi\)
\(12\) 35.8157 + 35.8157i 0.248720 + 0.248720i
\(13\) −27.8077 + 27.8077i −0.164542 + 0.164542i −0.784576 0.620033i \(-0.787119\pi\)
0.620033 + 0.784576i \(0.287119\pi\)
\(14\) 61.6638i 0.314611i
\(15\) −32.6150 + 154.888i −0.144956 + 0.688391i
\(16\) −64.0000 −0.250000
\(17\) −6.97609 6.97609i −0.0241387 0.0241387i 0.694934 0.719073i \(-0.255433\pi\)
−0.719073 + 0.694934i \(0.755433\pi\)
\(18\) 81.8272 81.8272i 0.252553 0.252553i
\(19\) 581.940i 1.61202i −0.591901 0.806011i \(-0.701622\pi\)
0.591901 0.806011i \(-0.298378\pi\)
\(20\) −109.246 167.527i −0.273116 0.418817i
\(21\) −138.033 −0.313001
\(22\) −267.283 267.283i −0.552237 0.552237i
\(23\) −77.9968 + 77.9968i −0.147442 + 0.147442i
\(24\) 143.263i 0.248720i
\(25\) 252.039 571.928i 0.403262 0.915084i
\(26\) 111.231 0.164542
\(27\) 545.803 + 545.803i 0.748700 + 0.748700i
\(28\) 123.328 123.328i 0.157306 0.157306i
\(29\) 1422.24i 1.69113i −0.533871 0.845566i \(-0.679263\pi\)
0.533871 0.845566i \(-0.320737\pi\)
\(30\) 375.006 244.546i 0.416673 0.271717i
\(31\) −109.874 −0.114333 −0.0571666 0.998365i \(-0.518207\pi\)
−0.0571666 + 0.998365i \(0.518207\pi\)
\(32\) 128.000 + 128.000i 0.125000 + 0.125000i
\(33\) 598.307 598.307i 0.549409 0.549409i
\(34\) 27.9044i 0.0241387i
\(35\) 533.340 + 112.306i 0.435380 + 0.0916786i
\(36\) −327.309 −0.252553
\(37\) 347.767 + 347.767i 0.254030 + 0.254030i 0.822621 0.568591i \(-0.192511\pi\)
−0.568591 + 0.822621i \(0.692511\pi\)
\(38\) −1163.88 + 1163.88i −0.806011 + 0.806011i
\(39\) 248.988i 0.163700i
\(40\) −116.561 + 553.546i −0.0728507 + 0.345966i
\(41\) −1500.74 −0.892764 −0.446382 0.894842i \(-0.647288\pi\)
−0.446382 + 0.894842i \(0.647288\pi\)
\(42\) 276.067 + 276.067i 0.156500 + 0.156500i
\(43\) 687.304 687.304i 0.371716 0.371716i −0.496386 0.868102i \(-0.665340\pi\)
0.868102 + 0.496386i \(0.165340\pi\)
\(44\) 1069.13i 0.552237i
\(45\) −558.708 856.766i −0.275905 0.423094i
\(46\) 311.987 0.147442
\(47\) −97.5012 97.5012i −0.0441382 0.0441382i 0.684693 0.728831i \(-0.259936\pi\)
−0.728831 + 0.684693i \(0.759936\pi\)
\(48\) −286.526 + 286.526i −0.124360 + 0.124360i
\(49\) 1925.70i 0.802040i
\(50\) −1647.93 + 639.777i −0.659173 + 0.255911i
\(51\) −62.4634 −0.0240151
\(52\) −222.461 222.461i −0.0822712 0.0822712i
\(53\) 2457.09 2457.09i 0.874722 0.874722i −0.118261 0.992983i \(-0.537732\pi\)
0.992983 + 0.118261i \(0.0377319\pi\)
\(54\) 2183.21i 0.748700i
\(55\) −2798.56 + 1824.98i −0.925145 + 0.603298i
\(56\) −493.310 −0.157306
\(57\) −2605.32 2605.32i −0.801884 0.801884i
\(58\) −2844.48 + 2844.48i −0.845566 + 0.845566i
\(59\) 3828.70i 1.09989i −0.835202 0.549943i \(-0.814649\pi\)
0.835202 0.549943i \(-0.185351\pi\)
\(60\) −1239.10 260.920i −0.344195 0.0724778i
\(61\) −5066.25 −1.36153 −0.680765 0.732502i \(-0.738352\pi\)
−0.680765 + 0.732502i \(0.738352\pi\)
\(62\) 219.748 + 219.748i 0.0571666 + 0.0571666i
\(63\) 630.722 630.722i 0.158912 0.158912i
\(64\) 512.000i 0.125000i
\(65\) 202.581 962.051i 0.0479481 0.227704i
\(66\) −2393.23 −0.549409
\(67\) 1522.51 + 1522.51i 0.339164 + 0.339164i 0.856052 0.516889i \(-0.172910\pi\)
−0.516889 + 0.856052i \(0.672910\pi\)
\(68\) 55.8087 55.8087i 0.0120694 0.0120694i
\(69\) 698.377i 0.146687i
\(70\) −842.068 1291.29i −0.171851 0.263529i
\(71\) −1397.47 −0.277221 −0.138611 0.990347i \(-0.544264\pi\)
−0.138611 + 0.990347i \(0.544264\pi\)
\(72\) 654.618 + 654.618i 0.126277 + 0.126277i
\(73\) 1262.48 1262.48i 0.236907 0.236907i −0.578661 0.815568i \(-0.696425\pi\)
0.815568 + 0.578661i \(0.196425\pi\)
\(74\) 1391.07i 0.254030i
\(75\) −1432.13 3688.87i −0.254601 0.655799i
\(76\) 4655.52 0.806011
\(77\) −2060.21 2060.21i −0.347480 0.347480i
\(78\) 497.975 497.975i 0.0818500 0.0818500i
\(79\) 5010.15i 0.802780i −0.915907 0.401390i \(-0.868527\pi\)
0.915907 0.401390i \(-0.131473\pi\)
\(80\) 1340.21 873.970i 0.209409 0.136558i
\(81\) 1573.07 0.239761
\(82\) 3001.47 + 3001.47i 0.446382 + 0.446382i
\(83\) 3638.73 3638.73i 0.528194 0.528194i −0.391839 0.920034i \(-0.628161\pi\)
0.920034 + 0.391839i \(0.128161\pi\)
\(84\) 1104.27i 0.156500i
\(85\) 241.349 + 50.8213i 0.0334047 + 0.00703409i
\(86\) −2749.21 −0.371716
\(87\) −6367.32 6367.32i −0.841237 0.841237i
\(88\) 2138.26 2138.26i 0.276118 0.276118i
\(89\) 12022.9i 1.51786i −0.651175 0.758928i \(-0.725724\pi\)
0.651175 0.758928i \(-0.274276\pi\)
\(90\) −596.117 + 2830.95i −0.0735947 + 0.349500i
\(91\) 857.363 0.103534
\(92\) −623.974 623.974i −0.0737210 0.0737210i
\(93\) −491.903 + 491.903i −0.0568740 + 0.0568740i
\(94\) 390.005i 0.0441382i
\(95\) 7946.84 + 12186.3i 0.880537 + 1.35028i
\(96\) 1146.10 0.124360
\(97\) 897.842 + 897.842i 0.0954238 + 0.0954238i 0.753207 0.657783i \(-0.228506\pi\)
−0.657783 + 0.753207i \(0.728506\pi\)
\(98\) −3851.39 + 3851.39i −0.401020 + 0.401020i
\(99\) 5467.75i 0.557877i
\(100\) 4575.42 + 2016.31i 0.457542 + 0.201631i
\(101\) 6434.40 0.630762 0.315381 0.948965i \(-0.397868\pi\)
0.315381 + 0.948965i \(0.397868\pi\)
\(102\) 124.927 + 124.927i 0.0120076 + 0.0120076i
\(103\) −13926.1 + 13926.1i −1.31267 + 1.31267i −0.393221 + 0.919444i \(0.628639\pi\)
−0.919444 + 0.393221i \(0.871361\pi\)
\(104\) 889.845i 0.0822712i
\(105\) 2890.53 1884.95i 0.262180 0.170971i
\(106\) −9828.37 −0.874722
\(107\) 8513.25 + 8513.25i 0.743581 + 0.743581i 0.973265 0.229684i \(-0.0737694\pi\)
−0.229684 + 0.973265i \(0.573769\pi\)
\(108\) −4366.42 + 4366.42i −0.374350 + 0.374350i
\(109\) 6247.33i 0.525826i −0.964820 0.262913i \(-0.915317\pi\)
0.964820 0.262913i \(-0.0846832\pi\)
\(110\) 9247.08 + 1947.17i 0.764221 + 0.160923i
\(111\) 3113.88 0.252730
\(112\) 986.621 + 986.621i 0.0786528 + 0.0786528i
\(113\) 2797.66 2797.66i 0.219098 0.219098i −0.589020 0.808118i \(-0.700486\pi\)
0.808118 + 0.589020i \(0.200486\pi\)
\(114\) 10421.3i 0.801884i
\(115\) 568.212 2698.43i 0.0429650 0.204040i
\(116\) 11377.9 0.845566
\(117\) −1137.71 1137.71i −0.0831114 0.0831114i
\(118\) −7657.41 + 7657.41i −0.549943 + 0.549943i
\(119\) 215.086i 0.0151886i
\(120\) 1956.37 + 3000.05i 0.135859 + 0.208337i
\(121\) 3218.99 0.219861
\(122\) 10132.5 + 10132.5i 0.680765 + 0.680765i
\(123\) −6718.74 + 6718.74i −0.444097 + 0.444097i
\(124\) 878.994i 0.0571666i
\(125\) 2532.21 + 15418.4i 0.162061 + 0.986781i
\(126\) −2522.89 −0.158912
\(127\) 8109.16 + 8109.16i 0.502769 + 0.502769i 0.912297 0.409529i \(-0.134307\pi\)
−0.409529 + 0.912297i \(0.634307\pi\)
\(128\) −1024.00 + 1024.00i −0.0625000 + 0.0625000i
\(129\) 6154.06i 0.369813i
\(130\) −2329.26 + 1518.94i −0.137826 + 0.0898782i
\(131\) 30412.4 1.77218 0.886090 0.463514i \(-0.153412\pi\)
0.886090 + 0.463514i \(0.153412\pi\)
\(132\) 4786.46 + 4786.46i 0.274705 + 0.274705i
\(133\) −8971.15 + 8971.15i −0.507160 + 0.507160i
\(134\) 6090.02i 0.339164i
\(135\) −18882.9 3976.21i −1.03610 0.218173i
\(136\) −223.235 −0.0120694
\(137\) −2657.43 2657.43i −0.141586 0.141586i 0.632761 0.774347i \(-0.281922\pi\)
−0.774347 + 0.632761i \(0.781922\pi\)
\(138\) 1396.75 1396.75i 0.0733436 0.0733436i
\(139\) 1120.78i 0.0580085i 0.999579 + 0.0290043i \(0.00923364\pi\)
−0.999579 + 0.0290043i \(0.990766\pi\)
\(140\) −898.451 + 4266.72i −0.0458393 + 0.217690i
\(141\) −873.019 −0.0439122
\(142\) 2794.94 + 2794.94i 0.138611 + 0.138611i
\(143\) −3716.25 + 3716.25i −0.181733 + 0.181733i
\(144\) 2618.47i 0.126277i
\(145\) 19421.8 + 29783.0i 0.923750 + 1.41655i
\(146\) −5049.91 −0.236907
\(147\) −8621.27 8621.27i −0.398967 0.398967i
\(148\) −2782.14 + 2782.14i −0.127015 + 0.127015i
\(149\) 16434.1i 0.740243i −0.928983 0.370122i \(-0.879316\pi\)
0.928983 0.370122i \(-0.120684\pi\)
\(150\) −4513.48 + 10242.0i −0.200599 + 0.455200i
\(151\) 25320.6 1.11051 0.555253 0.831682i \(-0.312621\pi\)
0.555253 + 0.831682i \(0.312621\pi\)
\(152\) −9311.04 9311.04i −0.403005 0.403005i
\(153\) 285.417 285.417i 0.0121926 0.0121926i
\(154\) 8240.83i 0.347480i
\(155\) 2300.86 1500.42i 0.0957694 0.0624524i
\(156\) −1991.90 −0.0818500
\(157\) 19257.5 + 19257.5i 0.781271 + 0.781271i 0.980045 0.198774i \(-0.0636961\pi\)
−0.198774 + 0.980045i \(0.563696\pi\)
\(158\) −10020.3 + 10020.3i −0.401390 + 0.401390i
\(159\) 22000.6i 0.870244i
\(160\) −4428.37 932.489i −0.172983 0.0364254i
\(161\) 2404.79 0.0927738
\(162\) −3146.15 3146.15i −0.119881 0.119881i
\(163\) 23703.8 23703.8i 0.892162 0.892162i −0.102564 0.994726i \(-0.532705\pi\)
0.994726 + 0.102564i \(0.0327048\pi\)
\(164\) 12005.9i 0.446382i
\(165\) −4358.71 + 20699.4i −0.160099 + 0.760309i
\(166\) −14554.9 −0.528194
\(167\) 907.579 + 907.579i 0.0325425 + 0.0325425i 0.723191 0.690648i \(-0.242675\pi\)
−0.690648 + 0.723191i \(0.742675\pi\)
\(168\) −2208.53 + 2208.53i −0.0782501 + 0.0782501i
\(169\) 27014.5i 0.945852i
\(170\) −381.056 584.341i −0.0131853 0.0202194i
\(171\) 23809.3 0.814242
\(172\) 5498.43 + 5498.43i 0.185858 + 0.185858i
\(173\) 21438.6 21438.6i 0.716314 0.716314i −0.251534 0.967848i \(-0.580935\pi\)
0.967848 + 0.251534i \(0.0809351\pi\)
\(174\) 25469.3i 0.841237i
\(175\) −12702.2 + 4931.39i −0.414767 + 0.161025i
\(176\) −8553.04 −0.276118
\(177\) −17141.0 17141.0i −0.547128 0.547128i
\(178\) −24045.9 + 24045.9i −0.758928 + 0.758928i
\(179\) 20851.2i 0.650767i −0.945582 0.325384i \(-0.894507\pi\)
0.945582 0.325384i \(-0.105493\pi\)
\(180\) 6854.13 4469.66i 0.211547 0.137952i
\(181\) −17991.9 −0.549185 −0.274593 0.961561i \(-0.588543\pi\)
−0.274593 + 0.961561i \(0.588543\pi\)
\(182\) −1714.73 1714.73i −0.0517669 0.0517669i
\(183\) −22681.4 + 22681.4i −0.677279 + 0.677279i
\(184\) 2495.90i 0.0737210i
\(185\) −12031.6 2533.51i −0.351544 0.0740251i
\(186\) 1967.61 0.0568740
\(187\) −932.294 932.294i −0.0266606 0.0266606i
\(188\) 780.010 780.010i 0.0220691 0.0220691i
\(189\) 16828.1i 0.471099i
\(190\) 8478.95 40266.3i 0.234874 1.11541i
\(191\) 35596.9 0.975764 0.487882 0.872910i \(-0.337770\pi\)
0.487882 + 0.872910i \(0.337770\pi\)
\(192\) −2292.20 2292.20i −0.0621800 0.0621800i
\(193\) −9427.48 + 9427.48i −0.253094 + 0.253094i −0.822238 0.569144i \(-0.807275\pi\)
0.569144 + 0.822238i \(0.307275\pi\)
\(194\) 3591.37i 0.0954238i
\(195\) −3400.12 5214.01i −0.0894181 0.137121i
\(196\) 15405.6 0.401020
\(197\) −28233.3 28233.3i −0.727492 0.727492i 0.242627 0.970120i \(-0.421991\pi\)
−0.970120 + 0.242627i \(0.921991\pi\)
\(198\) 10935.5 10935.5i 0.278938 0.278938i
\(199\) 2118.93i 0.0535069i 0.999642 + 0.0267534i \(0.00851690\pi\)
−0.999642 + 0.0267534i \(0.991483\pi\)
\(200\) −5118.22 13183.5i −0.127955 0.329587i
\(201\) 13632.4 0.337427
\(202\) −12868.8 12868.8i −0.315381 0.315381i
\(203\) −21925.2 + 21925.2i −0.532049 + 0.532049i
\(204\) 499.707i 0.0120076i
\(205\) 31426.7 20493.7i 0.747810 0.487656i
\(206\) 55704.3 1.31267
\(207\) −3191.13 3191.13i −0.0744739 0.0744739i
\(208\) 1779.69 1779.69i 0.0411356 0.0411356i
\(209\) 77771.2i 1.78043i
\(210\) −9550.98 2011.16i −0.216575 0.0456046i
\(211\) −86409.8 −1.94088 −0.970439 0.241348i \(-0.922410\pi\)
−0.970439 + 0.241348i \(0.922410\pi\)
\(212\) 19656.7 + 19656.7i 0.437361 + 0.437361i
\(213\) −6256.43 + 6256.43i −0.137901 + 0.137901i
\(214\) 34053.0i 0.743581i
\(215\) −5007.06 + 23778.4i −0.108319 + 0.514406i
\(216\) 17465.7 0.374350
\(217\) 1693.82 + 1693.82i 0.0359705 + 0.0359705i
\(218\) −12494.7 + 12494.7i −0.262913 + 0.262913i
\(219\) 11304.1i 0.235694i
\(220\) −14599.8 22388.5i −0.301649 0.462572i
\(221\) 387.977 0.00794368
\(222\) −6227.76 6227.76i −0.126365 0.126365i
\(223\) −53920.4 + 53920.4i −1.08428 + 1.08428i −0.0881796 + 0.996105i \(0.528105\pi\)
−0.996105 + 0.0881796i \(0.971895\pi\)
\(224\) 3946.48i 0.0786528i
\(225\) 23399.6 + 10311.8i 0.462215 + 0.203690i
\(226\) −11190.7 −0.219098
\(227\) −58185.9 58185.9i −1.12919 1.12919i −0.990309 0.138879i \(-0.955650\pi\)
−0.138879 0.990309i \(-0.544350\pi\)
\(228\) 20842.6 20842.6i 0.400942 0.400942i
\(229\) 102779.i 1.95989i 0.199260 + 0.979947i \(0.436146\pi\)
−0.199260 + 0.979947i \(0.563854\pi\)
\(230\) −6533.28 + 4260.43i −0.123502 + 0.0805374i
\(231\) −18446.9 −0.345701
\(232\) −22755.9 22755.9i −0.422783 0.422783i
\(233\) −7978.96 + 7978.96i −0.146972 + 0.146972i −0.776764 0.629792i \(-0.783140\pi\)
0.629792 + 0.776764i \(0.283140\pi\)
\(234\) 4550.85i 0.0831114i
\(235\) 3373.22 + 710.304i 0.0610813 + 0.0128620i
\(236\) 30629.6 0.549943
\(237\) −22430.2 22430.2i −0.399335 0.399335i
\(238\) 430.172 430.172i 0.00759431 0.00759431i
\(239\) 27188.7i 0.475985i −0.971267 0.237992i \(-0.923511\pi\)
0.971267 0.237992i \(-0.0764894\pi\)
\(240\) 2087.36 9912.82i 0.0362389 0.172098i
\(241\) 93444.7 1.60887 0.804434 0.594041i \(-0.202468\pi\)
0.804434 + 0.594041i \(0.202468\pi\)
\(242\) −6437.98 6437.98i −0.109931 0.109931i
\(243\) −37167.4 + 37167.4i −0.629434 + 0.629434i
\(244\) 40530.0i 0.680765i
\(245\) 26296.9 + 40325.7i 0.438099 + 0.671816i
\(246\) 26875.0 0.444097
\(247\) 16182.4 + 16182.4i 0.265246 + 0.265246i
\(248\) −1757.99 + 1757.99i −0.0285833 + 0.0285833i
\(249\) 32580.9i 0.525490i
\(250\) 25772.5 35901.3i 0.412360 0.574421i
\(251\) −86697.4 −1.37613 −0.688064 0.725650i \(-0.741539\pi\)
−0.688064 + 0.725650i \(0.741539\pi\)
\(252\) 5045.78 + 5045.78i 0.0794561 + 0.0794561i
\(253\) −10423.6 + 10423.6i −0.162846 + 0.162846i
\(254\) 32436.6i 0.502769i
\(255\) 1308.04 852.987i 0.0201159 0.0131178i
\(256\) 4096.00 0.0625000
\(257\) −43371.9 43371.9i −0.656663 0.656663i 0.297926 0.954589i \(-0.403705\pi\)
−0.954589 + 0.297926i \(0.903705\pi\)
\(258\) −12308.1 + 12308.1i −0.184907 + 0.184907i
\(259\) 10722.3i 0.159841i
\(260\) 7696.41 + 1620.65i 0.113852 + 0.0239741i
\(261\) 58189.1 0.854202
\(262\) −60824.7 60824.7i −0.886090 0.886090i
\(263\) 19131.9 19131.9i 0.276597 0.276597i −0.555152 0.831749i \(-0.687340\pi\)
0.831749 + 0.555152i \(0.187340\pi\)
\(264\) 19145.8i 0.274705i
\(265\) −17900.1 + 85007.2i −0.254896 + 1.21050i
\(266\) 35884.6 0.507160
\(267\) −53826.2 53826.2i −0.755042 0.755042i
\(268\) −12180.0 + 12180.0i −0.169582 + 0.169582i
\(269\) 93021.2i 1.28552i 0.766070 + 0.642758i \(0.222210\pi\)
−0.766070 + 0.642758i \(0.777790\pi\)
\(270\) 29813.5 + 45718.3i 0.408964 + 0.627137i
\(271\) −83220.8 −1.13316 −0.566582 0.824005i \(-0.691735\pi\)
−0.566582 + 0.824005i \(0.691735\pi\)
\(272\) 446.470 + 446.470i 0.00603468 + 0.00603468i
\(273\) 3838.38 3838.38i 0.0515018 0.0515018i
\(274\) 10629.7i 0.141586i
\(275\) 33682.8 76433.1i 0.445393 1.01069i
\(276\) −5587.02 −0.0733436
\(277\) −67889.2 67889.2i −0.884792 0.884792i 0.109225 0.994017i \(-0.465163\pi\)
−0.994017 + 0.109225i \(0.965163\pi\)
\(278\) 2241.57 2241.57i 0.0290043 0.0290043i
\(279\) 4495.35i 0.0577505i
\(280\) 10330.3 6736.54i 0.131765 0.0859253i
\(281\) 37774.9 0.478400 0.239200 0.970970i \(-0.423115\pi\)
0.239200 + 0.970970i \(0.423115\pi\)
\(282\) 1746.04 + 1746.04i 0.0219561 + 0.0219561i
\(283\) 19303.8 19303.8i 0.241030 0.241030i −0.576246 0.817276i \(-0.695483\pi\)
0.817276 + 0.576246i \(0.195483\pi\)
\(284\) 11179.8i 0.138611i
\(285\) 90135.4 + 18980.0i 1.10970 + 0.233671i
\(286\) 14865.0 0.181733
\(287\) 23135.3 + 23135.3i 0.280874 + 0.280874i
\(288\) −5236.94 + 5236.94i −0.0631383 + 0.0631383i
\(289\) 83423.7i 0.998835i
\(290\) 20722.3 98409.6i 0.246400 1.17015i
\(291\) 8039.21 0.0949353
\(292\) 10099.8 + 10099.8i 0.118453 + 0.118453i
\(293\) −28464.3 + 28464.3i −0.331562 + 0.331562i −0.853180 0.521617i \(-0.825329\pi\)
0.521617 + 0.853180i \(0.325329\pi\)
\(294\) 34485.1i 0.398967i
\(295\) 52283.9 + 80176.3i 0.600792 + 0.921302i
\(296\) 11128.5 0.127015
\(297\) 72941.8 + 72941.8i 0.826920 + 0.826920i
\(298\) −32868.3 + 32868.3i −0.370122 + 0.370122i
\(299\) 4337.82i 0.0485209i
\(300\) 29510.9 11457.0i 0.327899 0.127300i
\(301\) −21190.9 −0.233892
\(302\) −50641.3 50641.3i −0.555253 0.555253i
\(303\) 28806.6 28806.6i 0.313766 0.313766i
\(304\) 37244.1i 0.403005i
\(305\) 106092. 69183.6i 1.14046 0.743710i
\(306\) −1141.67 −0.0121926
\(307\) −10051.9 10051.9i −0.106652 0.106652i 0.651767 0.758419i \(-0.274028\pi\)
−0.758419 + 0.651767i \(0.774028\pi\)
\(308\) 16481.7 16481.7i 0.173740 0.173740i
\(309\) 124693.i 1.30594i
\(310\) −7602.56 1600.88i −0.0791109 0.0166585i
\(311\) −85798.1 −0.887068 −0.443534 0.896258i \(-0.646275\pi\)
−0.443534 + 0.896258i \(0.646275\pi\)
\(312\) 3983.80 + 3983.80i 0.0409250 + 0.0409250i
\(313\) −98508.8 + 98508.8i −1.00551 + 1.00551i −0.00552498 + 0.999985i \(0.501759\pi\)
−0.999985 + 0.00552498i \(0.998241\pi\)
\(314\) 77030.2i 0.781271i
\(315\) −4594.86 + 21820.9i −0.0463075 + 0.219913i
\(316\) 40081.2 0.401390
\(317\) 96104.3 + 96104.3i 0.956366 + 0.956366i 0.999087 0.0427210i \(-0.0136027\pi\)
−0.0427210 + 0.999087i \(0.513603\pi\)
\(318\) −44001.3 + 44001.3i −0.435122 + 0.435122i
\(319\) 190070.i 1.86781i
\(320\) 6991.76 + 10721.7i 0.0682789 + 0.104704i
\(321\) 76227.0 0.739774
\(322\) −4809.58 4809.58i −0.0463869 0.0463869i
\(323\) −4059.66 + 4059.66i −0.0389121 + 0.0389121i
\(324\) 12584.6i 0.119881i
\(325\) 8895.35 + 22912.6i 0.0842164 + 0.216924i
\(326\) −94815.4 −0.892162
\(327\) −27969.1 27969.1i −0.261567 0.261567i
\(328\) −24011.8 + 24011.8i −0.223191 + 0.223191i
\(329\) 3006.15i 0.0277727i
\(330\) 50116.2 32681.4i 0.460204 0.300105i
\(331\) −11449.0 −0.104499 −0.0522494 0.998634i \(-0.516639\pi\)
−0.0522494 + 0.998634i \(0.516639\pi\)
\(332\) 29109.8 + 29109.8i 0.264097 + 0.264097i
\(333\) −14228.4 + 14228.4i −0.128312 + 0.128312i
\(334\) 3630.32i 0.0325425i
\(335\) −52673.6 11091.6i −0.469357 0.0988332i
\(336\) 8834.13 0.0782501
\(337\) 142320. + 142320.i 1.25316 + 1.25316i 0.954295 + 0.298865i \(0.0966082\pi\)
0.298865 + 0.954295i \(0.403392\pi\)
\(338\) 54028.9 54028.9i 0.472926 0.472926i
\(339\) 25050.1i 0.217976i
\(340\) −406.571 + 1930.79i −0.00351705 + 0.0167024i
\(341\) −14683.7 −0.126278
\(342\) −47618.5 47618.5i −0.407121 0.407121i
\(343\) −66700.1 + 66700.1i −0.566942 + 0.566942i
\(344\) 21993.7i 0.185858i
\(345\) −9536.89 14624.6i −0.0801251 0.122870i
\(346\) −85754.3 −0.716314
\(347\) −6898.82 6898.82i −0.0572949 0.0572949i 0.677879 0.735174i \(-0.262899\pi\)
−0.735174 + 0.677879i \(0.762899\pi\)
\(348\) 50938.6 50938.6i 0.420619 0.420619i
\(349\) 120582.i 0.989989i −0.868896 0.494994i \(-0.835170\pi\)
0.868896 0.494994i \(-0.164830\pi\)
\(350\) 35267.2 + 15541.7i 0.287896 + 0.126871i
\(351\) −30355.0 −0.246386
\(352\) 17106.1 + 17106.1i 0.138059 + 0.138059i
\(353\) 99139.7 99139.7i 0.795606 0.795606i −0.186793 0.982399i \(-0.559809\pi\)
0.982399 + 0.186793i \(0.0598095\pi\)
\(354\) 68563.8i 0.547128i
\(355\) 29264.3 19083.6i 0.232210 0.151427i
\(356\) 96183.5 0.758928
\(357\) 962.932 + 962.932i 0.00755543 + 0.00755543i
\(358\) −41702.5 + 41702.5i −0.325384 + 0.325384i
\(359\) 66147.1i 0.513242i 0.966512 + 0.256621i \(0.0826092\pi\)
−0.966512 + 0.256621i \(0.917391\pi\)
\(360\) −22647.6 4768.94i −0.174750 0.0367974i
\(361\) −208333. −1.59861
\(362\) 35983.7 + 35983.7i 0.274593 + 0.274593i
\(363\) 14411.3 14411.3i 0.109368 0.109368i
\(364\) 6858.90i 0.0517669i
\(365\) −9197.24 + 43677.5i −0.0690354 + 0.327847i
\(366\) 90725.6 0.677279
\(367\) −109978. 109978.i −0.816531 0.816531i 0.169073 0.985604i \(-0.445923\pi\)
−0.985604 + 0.169073i \(0.945923\pi\)
\(368\) 4991.79 4991.79i 0.0368605 0.0368605i
\(369\) 61400.6i 0.450941i
\(370\) 18996.1 + 29130.2i 0.138759 + 0.212784i
\(371\) −75756.9 −0.550395
\(372\) −3935.22 3935.22i −0.0284370 0.0284370i
\(373\) −62523.6 + 62523.6i −0.449393 + 0.449393i −0.895153 0.445760i \(-0.852934\pi\)
0.445760 + 0.895153i \(0.352934\pi\)
\(374\) 3729.17i 0.0266606i
\(375\) 80364.4 + 57691.2i 0.571480 + 0.410249i
\(376\) −3120.04 −0.0220691
\(377\) 39549.2 + 39549.2i 0.278263 + 0.278263i
\(378\) −33656.3 + 33656.3i −0.235550 + 0.235550i
\(379\) 110606.i 0.770014i 0.922914 + 0.385007i \(0.125801\pi\)
−0.922914 + 0.385007i \(0.874199\pi\)
\(380\) −97490.5 + 63574.8i −0.675142 + 0.440268i
\(381\) 72608.8 0.500195
\(382\) −71193.7 71193.7i −0.487882 0.487882i
\(383\) −1184.54 + 1184.54i −0.00807515 + 0.00807515i −0.711133 0.703058i \(-0.751818\pi\)
0.703058 + 0.711133i \(0.251818\pi\)
\(384\) 9168.82i 0.0621800i
\(385\) 71276.3 + 15008.8i 0.480865 + 0.101257i
\(386\) 37709.9 0.253094
\(387\) 28120.1 + 28120.1i 0.187756 + 0.187756i
\(388\) −7182.74 + 7182.74i −0.0477119 + 0.0477119i
\(389\) 45967.0i 0.303771i 0.988398 + 0.151886i \(0.0485345\pi\)
−0.988398 + 0.151886i \(0.951465\pi\)
\(390\) −3627.79 + 17228.3i −0.0238513 + 0.113269i
\(391\) 1088.23 0.00711812
\(392\) −30811.2 30811.2i −0.200510 0.200510i
\(393\) 136155. 136155.i 0.881553 0.881553i
\(394\) 112933.i 0.727492i
\(395\) 68417.5 + 104917.i 0.438504 + 0.672436i
\(396\) −43742.0 −0.278938
\(397\) −159089. 159089.i −1.00939 1.00939i −0.999956 0.00943206i \(-0.996998\pi\)
−0.00943206 0.999956i \(-0.503002\pi\)
\(398\) 4237.85 4237.85i 0.0267534 0.0267534i
\(399\) 80327.0i 0.504564i
\(400\) −16130.5 + 36603.4i −0.100816 + 0.228771i
\(401\) 126144. 0.784475 0.392238 0.919864i \(-0.371701\pi\)
0.392238 + 0.919864i \(0.371701\pi\)
\(402\) −27264.8 27264.8i −0.168714 0.168714i
\(403\) 3055.34 3055.34i 0.0188127 0.0188127i
\(404\) 51475.2i 0.315381i
\(405\) −32941.5 + 21481.5i −0.200832 + 0.130965i
\(406\) 87700.9 0.532049
\(407\) 46476.0 + 46476.0i 0.280569 + 0.280569i
\(408\) −999.414 + 999.414i −0.00600379 + 0.00600379i
\(409\) 147744.i 0.883208i 0.897210 + 0.441604i \(0.145590\pi\)
−0.897210 + 0.441604i \(0.854410\pi\)
\(410\) −103841. 21866.0i −0.617733 0.130077i
\(411\) −23794.4 −0.140861
\(412\) −111409. 111409.i −0.656333 0.656333i
\(413\) −59023.1 + 59023.1i −0.346036 + 0.346036i
\(414\) 12764.5i 0.0744739i
\(415\) −26508.4 + 125888.i −0.153917 + 0.730950i
\(416\) −7118.76 −0.0411356
\(417\) 5017.70 + 5017.70i 0.0288558 + 0.0288558i
\(418\) −155542. + 155542.i −0.890217 + 0.890217i
\(419\) 203624.i 1.15985i 0.814672 + 0.579923i \(0.196917\pi\)
−0.814672 + 0.579923i \(0.803083\pi\)
\(420\) 15079.6 + 23124.3i 0.0854854 + 0.131090i
\(421\) −113865. −0.642431 −0.321215 0.947006i \(-0.604091\pi\)
−0.321215 + 0.947006i \(0.604091\pi\)
\(422\) 172820. + 172820.i 0.970439 + 0.970439i
\(423\) 3989.13 3989.13i 0.0222945 0.0222945i
\(424\) 78627.0i 0.437361i
\(425\) −5748.07 + 2231.57i −0.0318232 + 0.0123547i
\(426\) 25025.7 0.137901
\(427\) 78101.1 + 78101.1i 0.428352 + 0.428352i
\(428\) −68106.0 + 68106.0i −0.371790 + 0.371790i
\(429\) 33275.0i 0.180802i
\(430\) 57570.9 37542.7i 0.311362 0.203043i
\(431\) −310369. −1.67080 −0.835400 0.549643i \(-0.814764\pi\)
−0.835400 + 0.549643i \(0.814764\pi\)
\(432\) −34931.4 34931.4i −0.187175 0.187175i
\(433\) −136164. + 136164.i −0.726248 + 0.726248i −0.969870 0.243622i \(-0.921664\pi\)
0.243622 + 0.969870i \(0.421664\pi\)
\(434\) 6775.26i 0.0359705i
\(435\) 220288. + 46386.4i 1.16416 + 0.245139i
\(436\) 49978.7 0.262913
\(437\) 45389.4 + 45389.4i 0.237680 + 0.237680i
\(438\) −22608.2 + 22608.2i −0.117847 + 0.117847i
\(439\) 297445.i 1.54339i −0.635990 0.771697i \(-0.719408\pi\)
0.635990 0.771697i \(-0.280592\pi\)
\(440\) −15577.4 + 73976.6i −0.0804617 + 0.382111i
\(441\) 78787.2 0.405115
\(442\) −775.955 775.955i −0.00397184 0.00397184i
\(443\) 196943. 196943.i 1.00354 1.00354i 0.00354489 0.999994i \(-0.498872\pi\)
0.999994 0.00354489i \(-0.00112838\pi\)
\(444\) 24911.0i 0.126365i
\(445\) 164183. + 251771.i 0.829100 + 1.27141i
\(446\) 215681. 1.08428
\(447\) −73575.0 73575.0i −0.368227 0.368227i
\(448\) −7892.97 + 7892.97i −0.0393264 + 0.0393264i
\(449\) 277579.i 1.37687i −0.725298 0.688435i \(-0.758298\pi\)
0.725298 0.688435i \(-0.241702\pi\)
\(450\) −26175.6 67422.9i −0.129262 0.332953i
\(451\) −200560. −0.986034
\(452\) 22381.3 + 22381.3i 0.109549 + 0.109549i
\(453\) 113360. 113360.i 0.552410 0.552410i
\(454\) 232744.i 1.12919i
\(455\) −17953.9 + 11708.0i −0.0867234 + 0.0565534i
\(456\) −83370.3 −0.400942
\(457\) 204991. + 204991.i 0.981527 + 0.981527i 0.999832 0.0183054i \(-0.00582713\pi\)
−0.0183054 + 0.999832i \(0.505827\pi\)
\(458\) 205558. 205558.i 0.979947 0.979947i
\(459\) 7615.14i 0.0361453i
\(460\) 21587.4 + 4545.70i 0.102020 + 0.0214825i
\(461\) −3099.86 −0.0145861 −0.00729306 0.999973i \(-0.502321\pi\)
−0.00729306 + 0.999973i \(0.502321\pi\)
\(462\) 36893.9 + 36893.9i 0.172850 + 0.172850i
\(463\) 62253.8 62253.8i 0.290405 0.290405i −0.546835 0.837240i \(-0.684168\pi\)
0.837240 + 0.546835i \(0.184168\pi\)
\(464\) 91023.5i 0.422783i
\(465\) 3583.55 17018.2i 0.0165732 0.0787059i
\(466\) 31915.8 0.146972
\(467\) 186901. + 186901.i 0.856993 + 0.856993i 0.990983 0.133990i \(-0.0427789\pi\)
−0.133990 + 0.990983i \(0.542779\pi\)
\(468\) 9101.69 9101.69i 0.0415557 0.0415557i
\(469\) 46941.7i 0.213409i
\(470\) −5325.82 8167.04i −0.0241097 0.0369717i
\(471\) 172431. 0.777271
\(472\) −61259.2 61259.2i −0.274971 0.274971i
\(473\) 91852.1 91852.1i 0.410551 0.410551i
\(474\) 89721.0i 0.399335i
\(475\) −332827. 146672.i −1.47514 0.650068i
\(476\) −1720.69 −0.00759431
\(477\) 100529. + 100529.i 0.441828 + 0.441828i
\(478\) −54377.5 + 54377.5i −0.237992 + 0.237992i
\(479\) 83978.2i 0.366012i −0.983112 0.183006i \(-0.941417\pi\)
0.983112 0.183006i \(-0.0585828\pi\)
\(480\) −24000.4 + 15650.9i −0.104168 + 0.0679294i
\(481\) −19341.2 −0.0835974
\(482\) −186889. 186889.i −0.804434 0.804434i
\(483\) 10766.2 10766.2i 0.0461494 0.0461494i
\(484\) 25751.9i 0.109931i
\(485\) −31062.3 6540.85i −0.132054 0.0278068i
\(486\) 148670. 0.629434
\(487\) −239611. 239611.i −1.01030 1.01030i −0.999946 0.0103487i \(-0.996706\pi\)
−0.0103487 0.999946i \(-0.503294\pi\)
\(488\) −81060.0 + 81060.0i −0.340382 + 0.340382i
\(489\) 212242.i 0.887594i
\(490\) 28057.7 133245.i 0.116858 0.554958i
\(491\) 58812.0 0.243951 0.121976 0.992533i \(-0.461077\pi\)
0.121976 + 0.992533i \(0.461077\pi\)
\(492\) −53749.9 53749.9i −0.222048 0.222048i
\(493\) −9921.69 + 9921.69i −0.0408218 + 0.0408218i
\(494\) 64729.5i 0.265246i
\(495\) −74666.4 114499.i −0.304730 0.467297i
\(496\) 7031.95 0.0285833
\(497\) 21543.4 + 21543.4i 0.0872169 + 0.0872169i
\(498\) −65161.8 + 65161.8i −0.262745 + 0.262745i
\(499\) 173676.i 0.697489i 0.937218 + 0.348745i \(0.113392\pi\)
−0.937218 + 0.348745i \(0.886608\pi\)
\(500\) −123348. + 20257.7i −0.493390 + 0.0810307i
\(501\) 8126.39 0.0323759
\(502\) 173395. + 173395.i 0.688064 + 0.688064i
\(503\) −11620.5 + 11620.5i −0.0459291 + 0.0459291i −0.729698 0.683769i \(-0.760339\pi\)
0.683769 + 0.729698i \(0.260339\pi\)
\(504\) 20183.1i 0.0794561i
\(505\) −134742. + 87866.8i −0.528348 + 0.344542i
\(506\) 41694.4 0.162846
\(507\) 120943. + 120943.i 0.470505 + 0.470505i
\(508\) −64873.3 + 64873.3i −0.251384 + 0.251384i
\(509\) 326727.i 1.26110i −0.776149 0.630550i \(-0.782829\pi\)
0.776149 0.630550i \(-0.217171\pi\)
\(510\) −4322.05 910.100i −0.0166169 0.00349904i
\(511\) −38924.6 −0.149067
\(512\) −8192.00 8192.00i −0.0312500 0.0312500i
\(513\) 317624. 317624.i 1.20692 1.20692i
\(514\) 173488.i 0.656663i
\(515\) 101452. 481795.i 0.382514 1.81655i
\(516\) 49232.5 0.184907
\(517\) −13030.2 13030.2i −0.0487494 0.0487494i
\(518\) −21444.6 + 21444.6i −0.0799207 + 0.0799207i
\(519\) 191959.i 0.712647i
\(520\) −12151.5 18634.1i −0.0449391 0.0689131i
\(521\) 397121. 1.46301 0.731505 0.681836i \(-0.238818\pi\)
0.731505 + 0.681836i \(0.238818\pi\)
\(522\) −116378. 116378.i −0.427101 0.427101i
\(523\) 299724. 299724.i 1.09577 1.09577i 0.100866 0.994900i \(-0.467839\pi\)
0.994900 0.100866i \(-0.0321613\pi\)
\(524\) 243299.i 0.886090i
\(525\) −34789.8 + 78945.0i −0.126221 + 0.286422i
\(526\) −76527.7 −0.276597
\(527\) 766.493 + 766.493i 0.00275986 + 0.00275986i
\(528\) −38291.6 + 38291.6i −0.137352 + 0.137352i
\(529\) 12167.0i 0.0434783i
\(530\) 205815. 134214.i 0.732697 0.477800i
\(531\) 156646. 0.555559
\(532\) −71769.2 71769.2i −0.253580 0.253580i
\(533\) 41732.0 41732.0i 0.146898 0.146898i
\(534\) 215305.i 0.755042i
\(535\) −294530. 62019.7i −1.02902 0.216682i
\(536\) 48720.2 0.169582
\(537\) −93350.2 93350.2i −0.323718 0.323718i
\(538\) 186042. 186042.i 0.642758 0.642758i
\(539\) 257353.i 0.885831i
\(540\) 31809.7 151064.i 0.109087 0.518050i
\(541\) −329750. −1.12665 −0.563326 0.826235i \(-0.690478\pi\)
−0.563326 + 0.826235i \(0.690478\pi\)
\(542\) 166442. + 166442.i 0.566582 + 0.566582i
\(543\) −80548.9 + 80548.9i −0.273187 + 0.273187i
\(544\) 1785.88i 0.00603468i
\(545\) 85312.3 + 130825.i 0.287222 + 0.440450i
\(546\) −15353.5 −0.0515018
\(547\) −306007. 306007.i −1.02272 1.02272i −0.999736 0.0229849i \(-0.992683\pi\)
−0.0229849 0.999736i \(-0.507317\pi\)
\(548\) 21259.4 21259.4i 0.0707931 0.0707931i
\(549\) 207279.i 0.687717i
\(550\) −220232. + 85500.7i −0.728039 + 0.282647i
\(551\) −827659. −2.72614
\(552\) 11174.0 + 11174.0i 0.0366718 + 0.0366718i
\(553\) −77236.2 + 77236.2i −0.252564 + 0.252564i
\(554\) 271557.i 0.884792i
\(555\) −65207.3 + 42522.5i −0.211695 + 0.138049i
\(556\) −8966.26 −0.0290043
\(557\) 272348. + 272348.i 0.877837 + 0.877837i 0.993311 0.115474i \(-0.0368387\pi\)
−0.115474 + 0.993311i \(0.536839\pi\)
\(558\) −8990.71 + 8990.71i −0.0288752 + 0.0288752i
\(559\) 38224.6i 0.122326i
\(560\) −34133.8 7187.60i −0.108845 0.0229197i
\(561\) −8347.69 −0.0265241
\(562\) −75549.8 75549.8i −0.239200 0.239200i
\(563\) −122342. + 122342.i −0.385974 + 0.385974i −0.873249 0.487275i \(-0.837991\pi\)
0.487275 + 0.873249i \(0.337991\pi\)
\(564\) 6984.15i 0.0219561i
\(565\) −20381.2 + 96789.8i −0.0638458 + 0.303202i
\(566\) −77215.4 −0.241030
\(567\) −24250.4 24250.4i −0.0754315 0.0754315i
\(568\) −22359.6 + 22359.6i −0.0693053 + 0.0693053i
\(569\) 190163.i 0.587355i −0.955905 0.293678i \(-0.905121\pi\)
0.955905 0.293678i \(-0.0948792\pi\)
\(570\) −142311. 218231.i −0.438014 0.671686i
\(571\) −167852. −0.514818 −0.257409 0.966303i \(-0.582869\pi\)
−0.257409 + 0.966303i \(0.582869\pi\)
\(572\) −29730.0 29730.0i −0.0908663 0.0908663i
\(573\) 159366. 159366.i 0.485384 0.485384i
\(574\) 92541.1i 0.280874i
\(575\) 24950.3 + 64266.8i 0.0754640 + 0.194380i
\(576\) 20947.8 0.0631383
\(577\) 170670. + 170670.i 0.512633 + 0.512633i 0.915332 0.402700i \(-0.131928\pi\)
−0.402700 + 0.915332i \(0.631928\pi\)
\(578\) −166847. + 166847.i −0.499417 + 0.499417i
\(579\) 84413.0i 0.251798i
\(580\) −238264. + 155375.i −0.708275 + 0.461875i
\(581\) −112189. −0.332352
\(582\) −16078.4 16078.4i −0.0474676 0.0474676i
\(583\) 328369. 328369.i 0.966107 0.966107i
\(584\) 40399.3i 0.118453i
\(585\) 39361.0 + 8288.31i 0.115015 + 0.0242189i
\(586\) 113857. 0.331562
\(587\) −125647. 125647.i −0.364651 0.364651i 0.500871 0.865522i \(-0.333013\pi\)
−0.865522 + 0.500871i \(0.833013\pi\)
\(588\) 68970.2 68970.2i 0.199483 0.199483i
\(589\) 63940.2i 0.184308i
\(590\) 55784.8 264921.i 0.160255 0.761047i
\(591\) −252798. −0.723768
\(592\) −22257.1 22257.1i −0.0635075 0.0635075i
\(593\) −8108.29 + 8108.29i −0.0230579 + 0.0230579i −0.718542 0.695484i \(-0.755190\pi\)
0.695484 + 0.718542i \(0.255190\pi\)
\(594\) 291767.i 0.826920i
\(595\) −2937.17 4504.09i −0.00829650 0.0127225i
\(596\) 131473. 0.370122
\(597\) 9486.35 + 9486.35i 0.0266165 + 0.0266165i
\(598\) −8675.63 + 8675.63i −0.0242604 + 0.0242604i
\(599\) 193242.i 0.538578i 0.963059 + 0.269289i \(0.0867887\pi\)
−0.963059 + 0.269289i \(0.913211\pi\)
\(600\) −81936.0 36107.8i −0.227600 0.100299i
\(601\) 6464.17 0.0178963 0.00894816 0.999960i \(-0.497152\pi\)
0.00894816 + 0.999960i \(0.497152\pi\)
\(602\) 42381.8 + 42381.8i 0.116946 + 0.116946i
\(603\) −62291.2 + 62291.2i −0.171314 + 0.171314i
\(604\) 202565.i 0.555253i
\(605\) −67408.4 + 43957.8i −0.184163 + 0.120095i
\(606\) −115226. −0.313766
\(607\) 417558. + 417558.i 1.13329 + 1.13329i 0.989627 + 0.143658i \(0.0458866\pi\)
0.143658 + 0.989627i \(0.454113\pi\)
\(608\) 74488.3 74488.3i 0.201503 0.201503i
\(609\) 196317.i 0.529325i
\(610\) −350550. 73816.0i −0.942087 0.198377i
\(611\) 5422.56 0.0145252
\(612\) 2283.34 + 2283.34i 0.00609631 + 0.00609631i
\(613\) 94239.1 94239.1i 0.250790 0.250790i −0.570505 0.821294i \(-0.693252\pi\)
0.821294 + 0.570505i \(0.193252\pi\)
\(614\) 40207.5i 0.106652i
\(615\) 48946.5 232446.i 0.129411 0.614570i
\(616\) −65926.6 −0.173740
\(617\) −408173. 408173.i −1.07220 1.07220i −0.997182 0.0750142i \(-0.976100\pi\)
−0.0750142 0.997182i \(-0.523900\pi\)
\(618\) 249386. 249386.i 0.652972 0.652972i
\(619\) 402928.i 1.05159i 0.850611 + 0.525795i \(0.176232\pi\)
−0.850611 + 0.525795i \(0.823768\pi\)
\(620\) 12003.4 + 18406.9i 0.0312262 + 0.0478847i
\(621\) −85141.7 −0.220780
\(622\) 171596. + 171596.i 0.443534 + 0.443534i
\(623\) −185345. + 185345.i −0.477534 + 0.477534i
\(624\) 15935.2i 0.0409250i
\(625\) −263578. 288296.i −0.674759 0.738038i
\(626\) 394035. 1.00551
\(627\) −348179. 348179.i −0.885660 0.885660i
\(628\) −154060. + 154060.i −0.390635 + 0.390635i
\(629\) 4852.11i 0.0122639i
\(630\) 52831.5 34452.0i 0.133110 0.0868028i
\(631\) 495085. 1.24343 0.621714 0.783244i \(-0.286436\pi\)
0.621714 + 0.783244i \(0.286436\pi\)
\(632\) −80162.4 80162.4i −0.200695 0.200695i
\(633\) −386853. + 386853.i −0.965470 + 0.965470i
\(634\) 384417.i 0.956366i
\(635\) −280550. 59075.8i −0.695765 0.146508i
\(636\) 176005. 0.435122
\(637\) 53549.1 + 53549.1i 0.131969 + 0.131969i
\(638\) −380141. + 380141.i −0.933905 + 0.933905i
\(639\) 57175.6i 0.140026i
\(640\) 7459.91 35427.0i 0.0182127 0.0864916i
\(641\) 130080. 0.316588 0.158294 0.987392i \(-0.449401\pi\)
0.158294 + 0.987392i \(0.449401\pi\)
\(642\) −152454. 152454.i −0.369887 0.369887i
\(643\) −83774.8 + 83774.8i −0.202624 + 0.202624i −0.801123 0.598499i \(-0.795764\pi\)
0.598499 + 0.801123i \(0.295764\pi\)
\(644\) 19238.3i 0.0463869i
\(645\) 84038.6 + 128871.i 0.202004 + 0.309768i
\(646\) 16238.7 0.0389121
\(647\) 159581. + 159581.i 0.381217 + 0.381217i 0.871541 0.490323i \(-0.163121\pi\)
−0.490323 + 0.871541i \(0.663121\pi\)
\(648\) 25169.2 25169.2i 0.0599403 0.0599403i
\(649\) 511673.i 1.21479i
\(650\) 28034.5 63615.9i 0.0663537 0.150570i
\(651\) 15166.3 0.0357864
\(652\) 189631. + 189631.i 0.446081 + 0.446081i
\(653\) 63954.6 63954.6i 0.149984 0.149984i −0.628127 0.778111i \(-0.716178\pi\)
0.778111 + 0.628127i \(0.216178\pi\)
\(654\) 111876.i 0.261567i
\(655\) −636861. + 415305.i −1.48444 + 0.968020i
\(656\) 96047.2 0.223191
\(657\) 51652.5 + 51652.5i 0.119663 + 0.119663i
\(658\) 6012.30 6012.30i 0.0138864 0.0138864i
\(659\) 52015.9i 0.119775i −0.998205 0.0598873i \(-0.980926\pi\)
0.998205 0.0598873i \(-0.0190741\pi\)
\(660\) −165595. 34869.7i −0.380154 0.0800497i
\(661\) 386314. 0.884173 0.442086 0.896972i \(-0.354238\pi\)
0.442086 + 0.896972i \(0.354238\pi\)
\(662\) 22898.0 + 22898.0i 0.0522494 + 0.0522494i
\(663\) 1736.96 1736.96i 0.00395151 0.00395151i
\(664\) 116439.i 0.264097i
\(665\) 65355.5 310372.i 0.147788 0.701841i
\(666\) 56913.7 0.128312
\(667\) 110930. + 110930.i 0.249344 + 0.249344i
\(668\) −7260.63 + 7260.63i −0.0162713 + 0.0162713i
\(669\) 482799.i 1.07873i
\(670\) 83164.0 + 127530.i 0.185262 + 0.284095i
\(671\) −677060. −1.50377
\(672\) −17668.3 17668.3i −0.0391251 0.0391251i
\(673\) 344390. 344390.i 0.760362 0.760362i −0.216026 0.976388i \(-0.569310\pi\)
0.976388 + 0.216026i \(0.0693095\pi\)
\(674\) 569281.i 1.25316i
\(675\) 449723. 174596.i 0.987047 0.383201i
\(676\) −216116. −0.472926
\(677\) 265651. + 265651.i 0.579608 + 0.579608i 0.934795 0.355187i \(-0.115583\pi\)
−0.355187 + 0.934795i \(0.615583\pi\)
\(678\) −50100.1 + 50100.1i −0.108988 + 0.108988i
\(679\) 27682.2i 0.0600428i
\(680\) 4674.73 3048.45i 0.0101097 0.00659266i
\(681\) −520992. −1.12341
\(682\) 29367.5 + 29367.5i 0.0631390 + 0.0631390i
\(683\) 292240. 292240.i 0.626467 0.626467i −0.320710 0.947177i \(-0.603922\pi\)
0.947177 + 0.320710i \(0.103922\pi\)
\(684\) 190474.i 0.407121i
\(685\) 91938.2 + 19359.6i 0.195936 + 0.0412586i
\(686\) 266801. 0.566942
\(687\) 460137. + 460137.i 0.974930 + 0.974930i
\(688\) −43987.4 + 43987.4i −0.0929291 + 0.0929291i
\(689\) 136652.i 0.287857i
\(690\) −10175.5 + 48323.0i −0.0213725 + 0.101498i
\(691\) 231240. 0.484292 0.242146 0.970240i \(-0.422149\pi\)
0.242146 + 0.970240i \(0.422149\pi\)
\(692\) 171509. + 171509.i 0.358157 + 0.358157i
\(693\) 84290.5 84290.5i 0.175514 0.175514i
\(694\) 27595.3i 0.0572949i
\(695\) −15305.2 23470.2i −0.0316861 0.0485899i
\(696\) −203754. −0.420619
\(697\) 10469.3 + 10469.3i 0.0215502 + 0.0215502i
\(698\) −241163. + 241163.i −0.494994 + 0.494994i
\(699\) 71443.0i 0.146219i
\(700\) −39451.1 101618.i −0.0805125 0.207383i
\(701\) 238530. 0.485407 0.242704 0.970101i \(-0.421966\pi\)
0.242704 + 0.970101i \(0.421966\pi\)
\(702\) 60710.0 + 60710.0i 0.123193 + 0.123193i
\(703\) 202380. 202380.i 0.409502 0.409502i
\(704\) 68424.3i 0.138059i
\(705\) 18281.8 11921.8i 0.0367824 0.0239862i
\(706\) −396559. −0.795606
\(707\) −99192.4 99192.4i −0.198445 0.198445i
\(708\) 137128. 137128.i 0.273564 0.273564i
\(709\) 360860.i 0.717872i −0.933362 0.358936i \(-0.883140\pi\)
0.933362 0.358936i \(-0.116860\pi\)
\(710\) −96695.7 20361.4i −0.191818 0.0403915i
\(711\) 204983. 0.405489
\(712\) −192367. 192367.i −0.379464 0.379464i
\(713\) 8569.84 8569.84i 0.0168575 0.0168575i
\(714\) 3851.73i 0.00755543i
\(715\) 27073.1 128570.i 0.0529574 0.251494i
\(716\) 166810. 0.325384
\(717\) −121723. 121723.i −0.236774 0.236774i
\(718\) 132294. 132294.i 0.256621 0.256621i
\(719\) 687332.i 1.32956i 0.747038 + 0.664781i \(0.231475\pi\)
−0.747038 + 0.664781i \(0.768525\pi\)
\(720\) 35757.3 + 54833.0i 0.0689762 + 0.105774i
\(721\) 429367. 0.825958
\(722\) 416666. + 416666.i 0.799307 + 0.799307i
\(723\) 418348. 418348.i 0.800316 0.800316i
\(724\) 143935.i 0.274593i
\(725\) −813420. 358461.i −1.54753 0.681970i
\(726\) −57645.2 −0.109368
\(727\) 77256.9 + 77256.9i 0.146173 + 0.146173i 0.776406 0.630233i \(-0.217041\pi\)
−0.630233 + 0.776406i \(0.717041\pi\)
\(728\) 13717.8 13717.8i 0.0258834 0.0258834i
\(729\) 460213.i 0.865972i
\(730\) 105749. 68960.5i 0.198441 0.129406i
\(731\) −9589.38 −0.0179455
\(732\) −181451. 181451.i −0.338640 0.338640i
\(733\) −377934. + 377934.i −0.703409 + 0.703409i −0.965141 0.261731i \(-0.915707\pi\)
0.261731 + 0.965141i \(0.415707\pi\)
\(734\) 439911.i 0.816531i
\(735\) 298267. + 62806.6i 0.552116 + 0.116260i
\(736\) −19967.2 −0.0368605
\(737\) 203470. + 203470.i 0.374597 + 0.374597i
\(738\) −122801. + 122801.i −0.225470 + 0.225470i
\(739\) 65835.1i 0.120550i −0.998182 0.0602752i \(-0.980802\pi\)
0.998182 0.0602752i \(-0.0191978\pi\)
\(740\) 20268.1 96252.6i 0.0370125 0.175772i
\(741\) 144896. 0.263888
\(742\) 151514. + 151514.i 0.275197 + 0.275197i
\(743\) −121704. + 121704.i −0.220459 + 0.220459i −0.808692 0.588233i \(-0.799824\pi\)
0.588233 + 0.808692i \(0.299824\pi\)
\(744\) 15740.9i 0.0284370i
\(745\) 224421. + 344145.i 0.404344 + 0.620053i
\(746\) 250094. 0.449393
\(747\) 148874. + 148874.i 0.266794 + 0.266794i
\(748\) 7458.35 7458.35i 0.0133303 0.0133303i
\(749\) 262480.i 0.467878i
\(750\) −45346.4 276111.i −0.0806158 0.490864i
\(751\) 121197. 0.214888 0.107444 0.994211i \(-0.465733\pi\)
0.107444 + 0.994211i \(0.465733\pi\)
\(752\) 6240.08 + 6240.08i 0.0110345 + 0.0110345i
\(753\) −388141. + 388141.i −0.684541 + 0.684541i
\(754\) 158197.i 0.278263i
\(755\) −530236. + 345773.i −0.930198 + 0.606593i
\(756\) 134625. 0.235550
\(757\) 547316. + 547316.i 0.955095 + 0.955095i 0.999034 0.0439395i \(-0.0139909\pi\)
−0.0439395 + 0.999034i \(0.513991\pi\)
\(758\) 221211. 221211.i 0.385007 0.385007i
\(759\) 93332.0i 0.162012i
\(760\) 322131. + 67831.6i 0.557705 + 0.117437i
\(761\) 652879. 1.12736 0.563681 0.825992i \(-0.309385\pi\)
0.563681 + 0.825992i \(0.309385\pi\)
\(762\) −145218. 145218.i −0.250097 0.250097i
\(763\) −96308.6 + 96308.6i −0.165431 + 0.165431i
\(764\) 284775.i 0.487882i
\(765\) −2079.28 + 9874.47i −0.00355297 + 0.0168730i
\(766\) 4738.14 0.00807515
\(767\) 106467. + 106467.i 0.180978 + 0.180978i
\(768\) 18337.6 18337.6i 0.0310900 0.0310900i
\(769\) 322701.i 0.545692i 0.962058 + 0.272846i \(0.0879649\pi\)
−0.962058 + 0.272846i \(0.912035\pi\)
\(770\) −112535. 172570.i −0.189804 0.291061i
\(771\) −388349. −0.653301
\(772\) −75419.8 75419.8i −0.126547 0.126547i
\(773\) −684980. + 684980.i −1.14636 + 1.14636i −0.159091 + 0.987264i \(0.550856\pi\)
−0.987264 + 0.159091i \(0.949144\pi\)
\(774\) 112480.i 0.187756i
\(775\) −27692.6 + 62840.1i −0.0461063 + 0.104625i
\(776\) 28731.0 0.0477119
\(777\) −48003.4 48003.4i −0.0795116 0.0795116i
\(778\) 91933.9 91933.9i 0.151886 0.151886i
\(779\) 873338.i 1.43916i
\(780\) 41712.1 27201.0i 0.0685603 0.0447090i
\(781\) −186760. −0.306183
\(782\) −2176.45 2176.45i −0.00355906 0.00355906i
\(783\) 776264. 776264.i 1.26615 1.26615i
\(784\) 123245.i 0.200510i
\(785\) −666247. 140293.i −1.08117 0.227665i
\(786\) −544620. −0.881553
\(787\) 455092. + 455092.i 0.734768 + 0.734768i 0.971560 0.236792i \(-0.0760961\pi\)
−0.236792 + 0.971560i \(0.576096\pi\)
\(788\) 225866. 225866.i 0.363746 0.363746i
\(789\) 171306.i 0.275181i
\(790\) 72998.6 346669.i 0.116966 0.555470i
\(791\) −86257.3 −0.137861
\(792\) 87484.0 + 87484.0i 0.139469 + 0.139469i
\(793\) 140881. 140881.i 0.224029 0.224029i
\(794\) 636354.i 1.00939i
\(795\) 300436. + 460712.i 0.475354 + 0.728946i
\(796\) −16951.4 −0.0267534
\(797\) 641033. + 641033.i 1.00917 + 1.00917i 0.999958 + 0.00921058i \(0.00293186\pi\)
0.00921058 + 0.999958i \(0.497068\pi\)
\(798\) 160654. 160654.i 0.252282 0.252282i
\(799\) 1360.35i 0.00213088i
\(800\) 105468. 40945.8i 0.164793 0.0639777i
\(801\) 491902. 0.766679
\(802\) −252289. 252289.i −0.392238 0.392238i
\(803\) 168719. 168719.i 0.261657 0.261657i
\(804\) 109059.i 0.168714i
\(805\) −50358.4 + 32839.3i −0.0777105 + 0.0506760i
\(806\) −12221.4 −0.0188127
\(807\) 416452. + 416452.i 0.639467 + 0.639467i
\(808\) 102950. 102950.i 0.157690 0.157690i
\(809\) 475560.i 0.726621i 0.931668 + 0.363311i \(0.118354\pi\)
−0.931668 + 0.363311i \(0.881646\pi\)
\(810\) 108846. + 22919.9i 0.165899 + 0.0349335i
\(811\) 555596. 0.844729 0.422364 0.906426i \(-0.361200\pi\)
0.422364 + 0.906426i \(0.361200\pi\)
\(812\) −175402. 175402.i −0.266025 0.266025i
\(813\) −372576. + 372576.i −0.563682 + 0.563682i
\(814\) 185904.i 0.280569i
\(815\) −172684. + 820074.i −0.259979 + 1.23463i
\(816\) 3997.66 0.00600379
\(817\) −399969. 399969.i −0.599215 0.599215i
\(818\) 295488. 295488.i 0.441604 0.441604i
\(819\) 35077.8i 0.0522956i
\(820\) 163950. + 251414.i 0.243828 + 0.373905i
\(821\) −648338. −0.961867 −0.480934 0.876757i \(-0.659702\pi\)
−0.480934 + 0.876757i \(0.659702\pi\)
\(822\) 47588.9 + 47588.9i 0.0704306 + 0.0704306i
\(823\) −421156. + 421156.i −0.621790 + 0.621790i −0.945989 0.324199i \(-0.894905\pi\)
0.324199 + 0.945989i \(0.394905\pi\)
\(824\) 445634.i 0.656333i
\(825\) −191392. 492985.i −0.281200 0.724312i
\(826\) 236092. 0.346036
\(827\) 231159. + 231159.i 0.337986 + 0.337986i 0.855609 0.517623i \(-0.173183\pi\)
−0.517623 + 0.855609i \(0.673183\pi\)
\(828\) 25529.0 25529.0i 0.0372369 0.0372369i
\(829\) 1.21019e6i 1.76095i 0.474096 + 0.880473i \(0.342775\pi\)
−0.474096 + 0.880473i \(0.657225\pi\)
\(830\) 304793. 198759.i 0.442434 0.288516i
\(831\) −607875. −0.880262
\(832\) 14237.5 + 14237.5i 0.0205678 + 0.0205678i
\(833\) −13433.8 + 13433.8i −0.0193602 + 0.0193602i
\(834\) 20070.8i 0.0288558i
\(835\) −31399.2 6611.78i −0.0450345 0.00948299i
\(836\) 622169. 0.890217
\(837\) −59969.7 59969.7i −0.0856014 0.0856014i
\(838\) 407247. 407247.i 0.579923 0.579923i
\(839\) 286832.i 0.407477i 0.979025 + 0.203739i \(0.0653093\pi\)
−0.979025 + 0.203739i \(0.934691\pi\)
\(840\) 16089.3 76407.8i 0.0228023 0.108288i
\(841\) −1.31549e6 −1.85993
\(842\) 227730. + 227730.i 0.321215 + 0.321215i
\(843\) 169117. 169117.i 0.237975 0.237975i
\(844\) 691278.i 0.970439i
\(845\) −368904. 565706.i −0.516654 0.792278i
\(846\) −15956.5 −0.0222945
\(847\) −49623.8 49623.8i −0.0691708 0.0691708i
\(848\) −157254. + 157254.i −0.218680 + 0.218680i
\(849\) 172845.i 0.239796i
\(850\) 15959.3 + 7032.99i 0.0220890 + 0.00973424i
\(851\) −54249.4 −0.0749094
\(852\) −50051.4 50051.4i −0.0689505 0.0689505i
\(853\) 648590. 648590.i 0.891399 0.891399i −0.103256 0.994655i \(-0.532926\pi\)
0.994655 + 0.103256i \(0.0329261\pi\)
\(854\) 312404.i 0.428352i
\(855\) −498586. + 325134.i −0.682037 + 0.444765i
\(856\) 272424. 0.371790
\(857\) 220314. + 220314.i 0.299972 + 0.299972i 0.841003 0.541031i \(-0.181966\pi\)
−0.541031 + 0.841003i \(0.681966\pi\)
\(858\) 66550.0 66550.0i 0.0904011 0.0904011i
\(859\) 52637.7i 0.0713363i 0.999364 + 0.0356682i \(0.0113559\pi\)
−0.999364 + 0.0356682i \(0.988644\pi\)
\(860\) −190227. 40056.4i −0.257203 0.0541596i
\(861\) 207152. 0.279436
\(862\) 620739. + 620739.i 0.835400 + 0.835400i
\(863\) 949999. 949999.i 1.27556 1.27556i 0.332435 0.943126i \(-0.392130\pi\)
0.943126 0.332435i \(-0.107870\pi\)
\(864\) 139725.i 0.187175i
\(865\) −156182. + 741703.i −0.208736 + 0.991283i
\(866\) 544654. 0.726248
\(867\) −373485. 373485.i −0.496861 0.496861i
\(868\) −13550.5 + 13550.5i −0.0179853 + 0.0179853i
\(869\) 669563.i 0.886649i
\(870\) −347803. 533349.i −0.459510 0.704649i
\(871\) −84674.6 −0.111614
\(872\) −99957.4 99957.4i −0.131456 0.131456i
\(873\) −36734.0 + 36734.0i −0.0481992 + 0.0481992i
\(874\) 181558.i 0.237680i
\(875\) 198654. 276726.i 0.259466 0.361439i
\(876\) 90433.0 0.117847
\(877\) −534065. 534065.i −0.694376 0.694376i 0.268816 0.963192i \(-0.413368\pi\)
−0.963192 + 0.268816i \(0.913368\pi\)
\(878\) −594889. + 594889.i −0.771697 + 0.771697i
\(879\) 254867.i 0.329865i
\(880\) 179108. 116798.i 0.231286 0.150825i
\(881\) −1.00777e6 −1.29841 −0.649204 0.760614i \(-0.724898\pi\)
−0.649204 + 0.760614i \(0.724898\pi\)
\(882\) −157574. 157574.i −0.202558 0.202558i
\(883\) 522706. 522706.i 0.670403 0.670403i −0.287406 0.957809i \(-0.592793\pi\)
0.957809 + 0.287406i \(0.0927929\pi\)
\(884\) 3103.82i 0.00397184i
\(885\) 593020. + 124873.i 0.757151 + 0.159435i
\(886\) −787774. −1.00354
\(887\) −511630. 511630.i −0.650292 0.650292i 0.302771 0.953063i \(-0.402088\pi\)
−0.953063 + 0.302771i \(0.902088\pi\)
\(888\) 49822.1 49822.1i 0.0631824 0.0631824i
\(889\) 250021.i 0.316353i
\(890\) 175176. 831906.i 0.221154 1.05025i
\(891\) 210227. 0.264810
\(892\) −431363. 431363.i −0.542142 0.542142i
\(893\) −56739.8 + 56739.8i −0.0711517 + 0.0711517i
\(894\) 294300.i 0.368227i
\(895\) 284740. + 436643.i 0.355470 + 0.545105i
\(896\) 31571.9 0.0393264
\(897\) −19420.2 19420.2i −0.0241362 0.0241362i
\(898\) −555157. + 555157.i −0.688435 + 0.688435i
\(899\) 156268.i 0.193353i
\(900\) −82494.6 + 187197.i −0.101845 + 0.231107i
\(901\) −34281.8 −0.0422293
\(902\) 401121. + 401121.i 0.493017 + 0.493017i
\(903\) −94870.8 + 94870.8i −0.116347 + 0.116347i
\(904\) 89525.3i 0.109549i
\(905\) 376765. 245693.i 0.460016 0.299982i
\(906\) −453438. −0.552410
\(907\) 784298. + 784298.i 0.953382 + 0.953382i 0.998961 0.0455791i \(-0.0145133\pi\)
−0.0455791 + 0.998961i \(0.514513\pi\)
\(908\) 465487. 465487.i 0.564594 0.564594i
\(909\) 263255.i 0.318602i
\(910\) 59323.8 + 12491.9i 0.0716384 + 0.0150850i
\(911\) −1.57547e6 −1.89834 −0.949171 0.314762i \(-0.898075\pi\)
−0.949171 + 0.314762i \(0.898075\pi\)
\(912\) 166741. + 166741.i 0.200471 + 0.200471i
\(913\) 486285. 486285.i 0.583377 0.583377i
\(914\) 819964.i 0.981527i
\(915\) 165236. 784701.i 0.197361 0.937264i
\(916\) −822230. −0.979947
\(917\) −468836. 468836.i −0.557548 0.557548i
\(918\) −15230.3 + 15230.3i −0.0180727 + 0.0180727i
\(919\) 575240.i 0.681111i 0.940224 + 0.340556i \(0.110615\pi\)
−0.940224 + 0.340556i \(0.889385\pi\)
\(920\) −34083.4 52266.2i −0.0402687 0.0617512i
\(921\) −90003.6 −0.106106
\(922\) 6199.71 + 6199.71i 0.00729306 + 0.00729306i
\(923\) 38860.4 38860.4i 0.0456146 0.0456146i
\(924\) 147576.i 0.172850i
\(925\) 286549. 111247.i 0.334900 0.130018i
\(926\) −249015. −0.290405
\(927\) −569766. 569766.i −0.663036 0.663036i
\(928\) 182047. 182047.i 0.211392 0.211392i
\(929\) 1.41732e6i 1.64225i −0.570752 0.821123i \(-0.693348\pi\)
0.570752 0.821123i \(-0.306652\pi\)
\(930\) −41203.5 + 26869.3i −0.0476396 + 0.0310663i
\(931\) −1.12064e6 −1.29290
\(932\) −63831.7 63831.7i −0.0734859 0.0734859i
\(933\) −384115. + 384115.i −0.441263 + 0.441263i
\(934\) 747603.i 0.856993i
\(935\) 32254.2 + 6791.83i 0.0368947 + 0.00776897i
\(936\) −36406.8 −0.0415557
\(937\) −1.10376e6 1.10376e6i −1.25717 1.25717i −0.952437 0.304735i \(-0.901432\pi\)
−0.304735 0.952437i \(-0.598568\pi\)
\(938\) −93883.5 + 93883.5i −0.106705 + 0.106705i
\(939\) 882040.i 1.00036i
\(940\) −5682.43 + 26985.7i −0.00643100 + 0.0305407i
\(941\) 305672. 0.345205 0.172602 0.984992i \(-0.444782\pi\)
0.172602 + 0.984992i \(0.444782\pi\)
\(942\) −344861. 344861.i −0.388636 0.388636i
\(943\) 117053. 117053.i 0.131631 0.131631i
\(944\) 245037.i 0.274971i
\(945\) 229801. + 352396.i 0.257329 + 0.394609i
\(946\) −367408. −0.410551
\(947\) 377220. + 377220.i 0.420624 + 0.420624i 0.885419 0.464794i \(-0.153872\pi\)
−0.464794 + 0.885419i \(0.653872\pi\)
\(948\) 179442. 179442.i 0.199667 0.199667i
\(949\) 70213.0i 0.0779624i
\(950\) 372312. + 958998.i 0.412534 + 1.06260i
\(951\) 860510. 0.951470
\(952\) 3441.38 + 3441.38i 0.00379716 + 0.00379716i
\(953\) −349391. + 349391.i −0.384703 + 0.384703i −0.872793 0.488090i \(-0.837694\pi\)
0.488090 + 0.872793i \(0.337694\pi\)
\(954\) 402114.i 0.441828i
\(955\) −745429. + 486103.i −0.817334 + 0.532993i
\(956\) 217510. 0.237992
\(957\) −850937. 850937.i −0.929124 0.929124i
\(958\) −167956. + 167956.i −0.183006 + 0.183006i
\(959\) 81933.6i 0.0890892i
\(960\) 79302.6 + 16698.9i 0.0860488 + 0.0181194i
\(961\) −911449. −0.986928
\(962\) 38682.4 + 38682.4i 0.0417987 + 0.0417987i
\(963\) −348308. + 348308.i −0.375587 + 0.375587i
\(964\) 747558.i 0.804434i
\(965\) 68679.9 326159.i 0.0737522 0.350247i
\(966\) −43064.6 −0.0461494
\(967\) 103657. + 103657.i 0.110853 + 0.110853i 0.760358 0.649505i \(-0.225024\pi\)
−0.649505 + 0.760358i \(0.725024\pi\)
\(968\) 51503.8 51503.8i 0.0549653 0.0549653i
\(969\) 36349.9i 0.0387129i
\(970\) 49043.0 + 75206.4i 0.0521235 + 0.0799302i
\(971\) −119158. −0.126381 −0.0631907 0.998001i \(-0.520128\pi\)
−0.0631907 + 0.998001i \(0.520128\pi\)
\(972\) −297339. 297339.i −0.314717 0.314717i
\(973\) 17277.9 17277.9i 0.0182501 0.0182501i
\(974\) 958443.i 1.01030i
\(975\) 142403. + 62754.6i 0.149799 + 0.0660140i
\(976\) 324240. 0.340382
\(977\) −747694. 747694.i −0.783312 0.783312i 0.197076 0.980388i \(-0.436855\pi\)
−0.980388 + 0.197076i \(0.936855\pi\)
\(978\) −424485. + 424485.i −0.443797 + 0.443797i
\(979\) 1.60676e6i 1.67643i
\(980\) −322606. + 210375.i −0.335908 + 0.219050i
\(981\) 255601. 0.265598
\(982\) −117624. 117624.i −0.121976 0.121976i
\(983\) 477597. 477597.i 0.494259 0.494259i −0.415386 0.909645i \(-0.636353\pi\)
0.909645 + 0.415386i \(0.136353\pi\)
\(984\) 215000.i 0.222048i
\(985\) 976776. + 205681.i 1.00675 + 0.211993i
\(986\) 39686.8 0.0408218
\(987\) 13458.4 + 13458.4i 0.0138153 + 0.0138153i
\(988\) −129459. + 129459.i −0.132623 + 0.132623i
\(989\) 107215.i 0.109613i
\(990\) −79665.9 + 378331.i −0.0812834 + 0.386013i
\(991\) 552759. 0.562844 0.281422 0.959584i \(-0.409194\pi\)
0.281422 + 0.959584i \(0.409194\pi\)
\(992\) −14063.9 14063.9i −0.0142917 0.0142917i
\(993\) −51256.7 + 51256.7i −0.0519819 + 0.0519819i
\(994\) 86173.5i 0.0872169i
\(995\) −28935.6 44372.1i −0.0292271 0.0448192i
\(996\) 260647. 0.262745
\(997\) −187575. 187575.i −0.188705 0.188705i 0.606431 0.795136i \(-0.292601\pi\)
−0.795136 + 0.606431i \(0.792601\pi\)
\(998\) 347351. 347351.i 0.348745 0.348745i
\(999\) 379624.i 0.380385i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 230.5.f.a.47.15 44
5.3 odd 4 inner 230.5.f.a.93.15 yes 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.5.f.a.47.15 44 1.1 even 1 trivial
230.5.f.a.93.15 yes 44 5.3 odd 4 inner